18th European Symposium on Computer Aided Process Engineering – ESCAPE 18
Bertrand Braunschweig and Xavier Joulia (Editors)
© 2008 Elsevier B.V./Ltd. All rights reserved.
Real time optimization of large scale processes:
control of an autorefrigerated CSTR
polymerization reactor
Eduardo C. Vasco de Toledoa, Delba N. C. Melob, Adriano P. Marianob and
Rubens Maciel Filhob
a
Petrobras SA, Paulínia Refinery (REPLAN), Rodovia SP 332 - KM 132, P.O. Box 1,
CP13140-000. Paulínia, SP-Brazil.
b
Faculty of Chemical Engineering, State University of Campinas (UNICAMP), CP6066,
CEP13083-970, FAX +551937883910. Campinas, SP-Brazil.
Abstract
The optimization and temperature control of an industrial CSTR polymerization reactor
connected to a semi-flooded horizontal condenser (autorefrigeration technology), where
bulk reactions take place via styrene free-radicals, is presented in this work. This work
introduces an investigation study of the optimization of polymerization reactor to
determine the optimal operating conditions and, in a second stage, advanced control
algorithms are evaluated. The optimal operating condition or the set-points are defined
in the optimization layer and then used in the advanced control layer. The real time
process integration is carried out with the two-layer approach, where the control is set in
a hierarchical structure and an optimization layer calculates the set-points to the
advanced controller, based on the Generic Predictive Control procedure, predictive
QGPC (model predictive controls with restrictions using optimization routine, SQP) and
the adaptive STQGPC (predictive algorithms coupled to the identification algorithm
RLS). The proposed two-layer approach for real time process integration, based on the
SQP method as the optimization algorithm showed to be very efficient to control the
reactor even with significant changes on the operating conditions, allowing to operate
the reactor with efficiency and safety.
Keywords: polymerization, dynamic modelling, optimization, control, real time.
1. Introduction
Nowadays there is a significant incentive to develop optimization strategies, especially
those related to real time process integration, where the process optimization is coupled
with a model-based advanced predictive control. This is especially true for large scale
processes as the polymerization one, where significant improvements and economics
can be obtained with these strategies. However, the proper operation of a
polymerization reactor that meets different product requirements is not an easy task,
because of the complex reaction mechanism, the dramatic increase in the viscosity of
reaction mixture and the highly nonlinear nature of polymerization processes. Besides,
there is a lack of on-line process sensors to measure polymer properties. Therefore,
sophisticated model based controllers are needed to ensure the safe and proper operation
of these processes [1-3].
Polymerization reactors are also usually characterized by problems in their refrigeration.
Difficulties for the heat transfer are due to properties variations, as viscosity, during the
reaction phase, what generate hot spots with different conditions of temperature and
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Vasco de Toledo et al.
concentration and consequent heterogeneity in the product. The traditional methods of
jacket and cooling coils or external heat exchanger present low efficiency especially in
the case of bulk polymerization reactions. An interesting alternative for the cooling of
this type of process is to have a condenser connected to the reactor, which makes use of
the solvent and/or reagents latent heat of vaporization as an effective mechanism to
remove heat from the reactor. To achieve this, the reflux rate of the condenser is used to
control its liquid level and, indirectly, control the reactor temperature. This control
strategy is termed auto-refrigerated reactor, largely utilized for a great variety of
exothermal reactions, including polymerization [4-10]. Thus, this work introduces an
investigation study about the real time process integration of an autorefrigerated
continuous polymerization reactor, where optimal operating conditions are determined
and, in a second stage, advanced control algorithms are evaluated.
2. Autorefrigerated polymerization reactor
2.1. System
The case study considered in this work is the bulk polymerization via styrene free
radicals, because this is a well-known process with many studies published in the
literature, besides its great industrial importance. The description and kinetics of the
reactions involved in the bulk polymerization of styrene via free radicals can be found
elsewhere [7-9].
The configuration of the continuous polymerization reactor connected to a semi-flooded
horizontal condenser is shown in Figure 1a. This technique of cooling by means of the
latent heat of vaporization involves two mechanisms that quickly respond to
temperature changes inside the polymerization reactor. In the first mechanism, the
cooling area of the condenser increases directly as a result of temperature increase in the
reactor, lowering the level of condensed monomer. In the second mechanism, the
volume of condensed monomer displaced from the condenser is fed back into the
reactor, generating an instantaneous cooling effect [7-9].
2.2. Process Model
A detailed deterministic mathematical model was formulated to represent in a more
realistic way the dynamic behaviour of the CSTR plus semi-flooded horizontal
condenser. It consists of an ordinary differential equation system that represents the
effects of volume contraction, auto acceleration (gel) and the effect of non-condensable
gases. The model also takes into account the variation of the physical properties, of the
reaction heat, of the global coefficient of heat transfer, and uses the Flory-Huggins
equation to describe the reactor pressure. Integration was obtained with the routine
LSODAR, used for the integration of stiff ODE systems.
Equations and more details about the modelling, dynamic behaviour and description of
the system operation are given in some published works [4-9].
2.3. Advanced Control and Real Time Optimization
The controlling of polymerization reactors is a difficult task due to the dynamic
characteristics of the system, which is complex and non-linear. This reactor presents
great heat exchange difficulties in practice due to the polymeric incrustation in the
reactor wall and the increase of reaction medium viscosity that makes the heat exchange
difficult when a traditional method is used. Moreover, there are difficulties in measuring
the polymers structural characteristics in real time. The difficulty in defining the several
objectives for the control of the reactor temperature, with the purpose of achieving the
desired products specifications and overcoming the inherent difficulties of these
Real time optimization of large scale processes: control of an autorefrigerated CSTR
polymerization reactor
3
processes, also makes this a complex task. However the semi-flooded horizontal
condenser showed to be an efficient refrigeration system for the CSTR reactor where
the bulk styrene free radical polymerization happens [7-9]. A temperature controller
connected to the reactor, operating in cascade with a level controller, associated to the
condenser, makes the temperature control. The system periodically purges the noncondensable gases from the condenser, which prevent the level of condensed fluid from
reaching critical values. This control scheme has proved to be efficient for this system
and more details can be obtained in elsewhere [7-9]. In Figure 1a, TC is the temperature
controller, NC the condenser level controller and V the valve that sends the condensate
back to the reactor (reflux rate of the condenser, Fc).
Although several studies on modelling and control have been made for such system it is
important to study the problem of control and optimization in a real fashion. The real
time process integration involving optimization and process control can be carried out
simultaneously or sequentially. The traditional structure is built in two layers, as seen in
Figure 1b. In this case, the optimization layer calculates the reference values used
sequentially by the advanced control layer.
Optimizer
- steady-state model
- objective function
-algorithm optimization
setpoints
Controller
-Convolution model
- objective function
-algorithms NLP
Identification
block
Process
measured inputs
Dynamic model
non-measured
inputs
(a)
measured
outputs
non-measured
outputs
(b)
Figure 1. (a) Scheme of a CSTR connected to a semi-flooded condenser. (b) Real time
process integration - two-layer structure
The polymerization reactor is a nonlinear multivariable system with a relatively large
number of operating variables that can be chosen as decision variables. The
optimization performance is dependent on the right choice, what is not a trivial task.
Besides, due to the nonlinearity of the system, local minimums can be found and the
solution trajectory can be a function of the initial estimates. Another point to be
considered is the interaction between variables and their impacts in the behaviour of the
process.
Therefore, in this work the real time process integration is carried out with the two-layer
approach, where the control is set in a hierarchical structure and an optimization layer
calculates the set-points to the advanced controller, based on the Generic Predictive
Control procedure, predictive QGPC (model predictive controls with restrictions using
optimization routine, SQP) and the adaptive STQGPC (predictive algorithms coupled to
the identification algorithm RLS).
The mathematical description of the optimization problem considered in this work can
be seen as follow:
4
Vasco de Toledo et al.
Objective function: min ( T
Tf
 Treference )2
subject to: 1) Fcmin ≤ Fc ≤ Fcmax ;
(1)
Fcmin = 0.7*Fc; Fcmax = 2.0*Fc;
2) model equations: steady-state.
Where Fc is the reflux rate of the condenser; T is the reactor temperature and the value
of Treference is specified to keep the conversion of the process in a suitable operating
range.
Therefore, the optimization is designed to minimize the temperature difference (TTreference) in face to new feed conditions (previously known) before they affect the
process. The result of the optimization is a new set-point sent to the advanced controller,
aiming a better performance of the controller under the new conditions.
With the control of the reactor temperature, indirectly the conversion is kept in a desired
range. However, it is important to stress that for a more accurate control of the polymer
properties, it is necessary to control other variables besides the temperature
(multivariable control).
The two-layer procedure allows to conciliate the larger computational time demanded
by the optimization layer with the control layer, aiming the real time process
integration.
3. Results
Regarding the control of the reactor, Figures 2 and 3, respectively, present the
supervisory and regulatory control of the system without the optimization layer (RTO).
The best performance of the long-range quadratic predictive algorithm (QGPC), over
the quadratic predictive adaptive algorithm (QSTGPC), is visibly noticeable.
523.6
532
523.4
530
523.2
QGPC
QSTGPC
523.0
T (K)
526
Supervisory Control - Set Point = 531.9 K
524
522.8
T (K)
QGPC
QSTGPC
528
522.6
Regulatory Control - Set Point = 521.9 K
522.4
Step Perturbation of 5% in Tf
522.2
522.0
522
521.8
0
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
time (s)
Figure 2. Supervisory control (without RTO).
0
5000
10000
15000
20000
25000
30000
time (s)
Figure 3. Regulatory control (without RTO).
However, the performances of both algorithms are superior to those of classical
algorithms reported in previous works [7-9]. As advanced controllers have more
complex algorithms with a greater number of tuneable parameters, they can interfere
more efficiently in the dynamic characteristics of the system.
Examples of the control of the reactor with the optimization layer can be seen in Figures
4 to 9. In all cases, the control was carried out with the QGPC algorithm, since the
previous analysis showed that this algorithm has a superior and more robust
performance in relation to the QSTGPC algorithm.
Real time optimization of large scale processes: control of an autorefrigerated CSTR
polymerization reactor
5
0.9140
523.5
0.9138
Real Time Optimization
523.0
0.9136
Step Perturbation of 5% in Tf
Real Time Optimization
0.9134
X
T (K)
522.5
522.0
0.9132
Step Perturbation of 5% in Tf
0.9130
0.9128
521.5
0.9126
521.0
0
5000
10000
15000
20000
25000
0.9124
30000
0
5000
10000
time (s)
15000
20000
25000
30000
time (s)
Figure 4. Temperature dynamic behaviour with
RTO. Directly controlled.
Figure 5. Conversion dynamic behaviour with
RTO. Indirectly controlled.
Figures 4 and 5 show the temperature and conversion dynamic profiles in close loop
when the feed temperature of the polymerization reactor (Tf) is altered by 5 %. Based
on the knowledge of the alteration in the feed condition of the reactor, the optimization
layer is activated and generates a new set point to the advanced controller, QGPPC,
aiming to keep the reactor temperature (indirectly the reactor conversion) close to the
value before the perturbation in Tf. In these Figures it is possible to observe that the
optimization layer (RTO) is able to provide the suitable set point to keep the
temperature and conversion values close to the desired values.
The next cases (Figures 6 and 7) present, respectively, the temperature and conversion
profiles when there is an alteration of 5 % in both feed concentration of monomers (Mf)
and feed temperature (Tf). The optimization layer is activated to generate a new set
point to the controller and despite the changes in the feed conditions, the two layer
strategy is again able to keep the reactor operating at the desired conditions.
530
0.916
529
0.915
Real Time Optimization
528
527
Step Perturbation of 5% in Tf and Mf
0.914
525
X
T (K)
526
0.913
Real Time Optimization
524
523
Step Perturbation of 5% in Tf and Mf
0.912
522
521
0.911
520
0
5000
10000
15000
20000
time (s)
Figure 6. Temperature dynamic behaviour
with RTO. Directly controlled.
0
10000
20000
30000
40000
50000
time (s)
Figure 7. Conversion dynamic behaviour with
RTO. Indirectly controlled.
In the sequence, Figures 8 and 9 show the case where there is a change in the reactor
temperature set point of 10o K (supervisory control) followed by an alteration of 5 % of
the feed temperature (Tf), with the optimization layer generating a new set point to keep
the reactor in the desired operating conditions. As in the previous cases, the control
based on the two layer approach successfully delivers its objectives.
6
Vasco de Toledo et al.
534
0.922
532
0.920
Real Time Optimization
528
526
Real Time Optimization
0.918
Supervisory Control - Set Point = 531.91 K
X
T (K)
530
Supervisory Control - Set Point = 531.91 K
0.916
RTO - Step Pertrubation of 5% in Tf
524
RTO - Step Pertrubation of 5% in Tf
0.914
522
520
0
10000
20000
30000
40000
50000
time (s)
Figure 8. Temperature dynamic behaviour
with RTO. Directly controlled.
0.912
0
20000
40000
60000
80000
100000
time (s)
Figure 9. Conversion dynamic behaviour with
RTO. Indirectly controlled.
The profiles of the manipulated variables are qualitatively similar to the controlled one
and, if necessary due to operating restrictions, their variation ranges can be reduced by
tuning the controller parameters.
Therefore, the results show that the two-layer approach (optimization layer and
advanced control) provides a robust, fast and efficient control of the autorefrigerated
polymerization reactor in face to alterations of the feed concentration and temperature,
as in the cases of supervisory and regulatory controls demanded during the operating
routines in an industrial plant.
4. Conclusions
The integration optimization and control in a real time fashion of the autorefrigerated
polymerization reactor was presented in this work, where the controllers QGPC /
QSTGPC and the SQP optimization method were employed. The optimization layer
was designed to keep the temperature and indirectly the conversion, close to the
reference values, independently of the perturbations in the process. Generally, the twolayer approach presented a good performance, being a good strategy to keep the
polymerization reactor operating at desired conditions suitable to produce polymers
under specifications.
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